In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular bounded domain Ω ⊂ Rn, n ≥ 3, we prove that if the mean curvature H of the boundary obeys the condition (Formula Presented) then Ω is a round ball.
Some sphere theorems in linear potential theory / Borghini, Stefano; Mascellani, Giovanni; Mazzieri, Lorenzo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6850. - 371:11(2019), pp. 7757-7790. [10.1090/tran/7637]
Some sphere theorems in linear potential theory
Borghini, Stefano;Mazzieri, Lorenzo
2019
Abstract
In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular bounded domain Ω ⊂ Rn, n ≥ 3, we prove that if the mean curvature H of the boundary obeys the condition (Formula Presented) then Ω is a round ball.File in questo prodotto:
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